1、TECHBICAL WOTES I?dTIOBAtlL ADVISORY COMMITTEE FOR AEROHAUTICS I_ No. 747 PROPELLCB ROTATIOB BOISE DUE TO TORQVE AWD THRUST By Arthur F. Dcrning Zcnglcy Memorial Acronnutical Laboratory W a sli i n g t on January 1940 Provided by IHSNot for ResaleNo reproduction or networking permitted without licen
2、se from IHS-,-,-ITAT 1 OIJAL ADV1 SORP C OHM ITTEE FOX AZROiTAUT IC S TECHITICAL :TOTE 3TO. 747 PErJPf;LLEI! ROTBTIOI By Arthur F, Deming Sound. pressures of the first four hnrmoi?ics of rota- tion noise from a full-scale two-blade propeller were measured aid are compared with values calculated from
3、 bution with constant tip speed and (2) for fixed space angles with varirtblo kip specd. .theory, The comparison is mad-e (1) for the space distri- A relation for rotztion noise from an clement of ra- dius developed by GstIn is extended to cover the entire progoller dlsk. Curves TC Givcn sbos.rirzg
4、the effect of number of ulndes on the rot?,tion noise, Propeller noise cam, in gencra.1, be divided into two ccssificctions: (1) rot?-tion noisc nnd (2) vortex noisc. The first is by fur the more intense, ?he second., as the name implies, is d.ue to the ediiing of vortices from the blades; and its i
5、ntensity and frequency sixctrum probably depend on angle of sttack, valoci-tjr, air turbulbnce, blade chorcl, and s3ape of the blzde sections frorr! hub $0 tip. The rotatioh iloisc is due to the pressure wave envel- oping each blado and movirig with it; tkc vortex noise,is due to pressure variations
6、 on the blade as a rcsmlt.of variations of circulatioa. It may be sirnr;.lx stated that the rotatioll noise is duo to thc coastm-i; nir force on the blades nnci that the vortex noise is duo to the vortices shed in thc wake. The rotation noise may be further divided into th.e rotatioil noise due (1)
7、to torque and thrust and (2) to blade thickness. The secoad case has been treated in a previous paper (reference 1). The effect of thickness on rotation noise is small except for the higher harmonics and small angles of cttack. Provided by IHSNot for ResaleNo reproduction or networking permitted wit
8、hout license from IHS-,-,-2 3TJ,A.C.A. Technioaf Xotc Bo. 747 !?%?e propoller rotation-noise thcorg (rcI“eroiicc 2) d-oos not chcck with experiment in some respects, especial- ly in tLZc d-etails of spati tribution and tine p of the harmonics ; does predict to a f degree of accuracy s s OTIild and m
9、aximuro, sound pres e general shape of the spa,tial distribution of sound pressure of the fun- daneztal and chc sccoild liarnionic for a two-blade propel- lor is fairly well given by theory. For highcr harmonics, the distribution is not so well given by theory. The use of G%s thcorg does, however, g
10、ive relatively accurate vrzl- ucs for thny magnitudes to be expected, bicli is perhaps all .that is required in sound. rbscarch whcrc one is deal- in:, with sound lcvcls in decibels instcad of percentages. Gutin (refeseacc 2) starts his derivation for the effect of torque and thrust with ant? arrive
11、s at the result Equation (1) employs the standard notation =sed in acous- tics, X, Y, and Z being the componclts of force ex- erted 18 the blade clecent on the medium. Some of the symbols used bg Gutin ?,re different from those used by the 17.B.C.A. in acoustizs; in order to avoid confusion, the fol
12、loving tsblc, whi.ch comperes acoustic symbols, has been included in this paper. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-E.A.C.A. Technical Mote Xo. 74-7 3 Item -.- h1ass dessitp of medium Velocit2- of sound Angular velocity Frequcnc;r, cycle
13、s per seconi Wave le2gth Dis-Lai?ce of microphone to ceatcr of propeller Mixmber of blades Oidsi*, of hrnonic Tlirus t Tot a1 ti1i-u.s t Yorqce Total toryue Pr 0102 13. e% rad ius Propcllcr tip radius Blade-B3le?:enL station Scctioi- vcl.oci%y Angli? ia disk from rofcranc Dirzction from front of dis
14、 Bosscl fuaction argiinicnt S 0 UII d $2 i c s s ii o HarLlOiliC pGWDT, Watts C on s t Si1 t s Gut in , - 3 v $=- R f h 1 n T Q QO R RO 9 B Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-4 3T.A.C.A. Tcchnical Xotc 60. ?47 i - S 3 1 i ct i % y Tis ts
15、Ib*y.tion exponent I - i 1 a, b, e, and f Bc?ssel fmction of ffrst v 2. ri 2 o f o r d e r qn Gnti-, in the course of his derfvation of cquatiolcl (21, dovslo2s the sclation for the soiand prcssilrc at a C?is-LL?unt goint d.uc to th3 torclue and the thrust from an aleccnt of rc:dius dR. This rclatio
16、ii, oxprcsscd in tho E.A.C.8. 8coustic nstco,tion, is Prom this relation, Guti:, studied ayroxixations, or- rives at the selc-tion given in equntioa (2). Fkc use of simple relations to represent the torque sild tha thrust dSs ti-ibucion makcs it quictl f or?,sible to integrate ovsr the entire disk.
17、An cqition resulting from this integration will show the cffcct of torque and thrust distribution 011 the sound pressurc of tCe harmonic comjloaents. By thc: use of and for t4;c thrust .?A inte- Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-B.A.C.A
18、. Technical IJote .330.747 5 grating with respect to R from 0 to Rd, The result is (a + l)(b + 1) 1 ” Ro (b - a) I and where the subscript o refers to the values at the tip and to intcgratcd valucs. dp and - dQ in equa- SuSstitution of tho values for - aIi d ii tion (3) gives Intcgrntion of equation
19、 (8) gi-res 1 (qn+ a+ l)(qn+ 3-1- 1) qmu, pqn = - To cos p (a 3- 1Mb-b 1) 2 x 4 ( 3qn -i- 2) ( 2qn f 4) ( qn + a 3- 5) ( qn + 2 + 5) J Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-6 B.A.C.A. Technical Bote ?TO, 747 TO where ab = qn sin -. it can b
20、c shown. that the argu- 2n B si0 p ment mo is equal to - A wave lengths contained ir? c distance equal to n tines the diarnctcr projected on the line to tho obscrver, C or the number of Equction (8) could have been integrated in terns of a series of Bossel functions, for which tables could be used;
21、but the expression resulting therefrom would be more euqbcrsomc to USG than equation (91, at, least for the snallcr v:lucs of qn, XEFEZElTCE CORD 1 TI OBS The conditions under which the calcalations for the sound pressures aad the expcrincntnl tcsts crc nadc are: Zunbsr of propeller blades n, 2. Bla
22、de rcdius to tiF Bo, 4.75 fcct. BZt:de section, E.A.3. 6, Elaxle zngle nt G.75E0 a, 5. Distz-ncc of nicrophone to propller center 2, 35 feet. Total thrust at propzll,tr sped of 1,700 r,p.n. L = O)Tn, 668 pounds. nD Total torque at propeller specd of 1,700 r.p.n* 251 pound-f eet. Specific acoustic rc
23、sistance pc, 42 gracs per SCC- ozcf centiucter“. The d?.t;z, for the polar cu-rvcs were obtclncd nt a con- strat propeller specd of 1,700 r.p.n. and with the aziriuth ailgle p betvreeil propeller axis nnd nicrophonc changed in steps of 15O, Tor, the spccd runs, the arglc wcs held at a coustznt vnluc
24、 of 120O for tlze fundanentnl, 110 for tSc second and the third harnonics, an6 102-1/2O for the fourth hp-rnonic, whilc the specd was varied fro3 r,ininur to nt-txhui. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-iJ.k.C.A, Technical ?Toto 30. 747
25、7 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-8 9.A.C.A. Techcical IJote 110. 747 plotted pqn Figure 5 shows the sound pressure against qn for the referezce coEditions given earlier with the thrust and the torque fixed. It will be realized the qn
26、 nust be a whole nunber; obviotzsly, values between whole r,ur.,bcrs have no practical neaning. For a two-blade propeller, the values of qn for the harnonics would be 2, 4, 6, 8, 10, 12, etc.; for a three- blade propeller, 3, 6, 9, 12, 15, 18, cto,.; for a four- blade propoller 4, 8, 12, 16, 20, 24,
27、 etc., Tor any value of ti? speed used, the sounl! pressure of all the harnonics for any coxlition can be esticsted fror; curves like those in figure 5. It nust be re:ienbcred that the sound pressure is proportiona,l to the torquo and the thrust as shown in equation (9) acd that figure 5 is plotted
28、for the given con- ditio:is wit11 = 110. POtlilER RADIATPED AS ROTATI017 EiOISE For noraal coditions, the power radiated as souild is largely rmde up of rotctfor noisc. The poiqer involved in the vortex noisc is relatively small except ot low values of Vo/c. This conclusion would be true for propell
29、ers with two or three blades; it is possible, however, that the power involved in vortex noise nay be equal to or even greater than that due to rotation noise for a large number of blades. The povrer in watts raciiated can be obtained by sub- stituting thc data given heroin in the relation see ref-
30、erencc 2) m For this relation, the data given by the polar curves of thc sound pressures can be used. These data were meas- ured at 15 intervals up to 3600, naking 24 vzlues for the conplctc polar circle. Since sound pressures were rnccsured on both sides of the Oo - 180 axis, the square of each pre
31、ssure neasurcd from 0 to 180 should be added,to the sq,unre of the corresponding pressure on the oppositc side of the axis and the nean of these two squares be taken. This conputation will resxlt in 12 values of pqn2 for the exparinentnl sound. pressure coiisis tent with the rcvlgc of the iiltcgral
32、0 to n. An inportnnt fact to rcnenbcr is Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Z.B.C.A. Tcchniccsl Xotc Eo. 747 9 which 2.10 naxirnu.1 vnluee of tkc sinusoidal sound pres- surcs cr?lculatcd for free space. The soun,;! pressurcs ;ici?.surcd.
33、 by the nicroF,lzo;?c on thc ground are double tlic! va1.10 that would be nccsurod in the sa2 relative locn- tioiis in frcc spce. If values vcrc tzkon from figure I, thcy nust therefore bo divided by n. Equation (LO) thcn bccoies, vith pqn as tho ricasured prcssurcs, yuation (9) PI Xa 18.2 These lis
34、ted values of power radiated by the first four harr;,oiics are Plotted oii sernilog Dnper 5n figure 6. The sum of the wattages for the first four hzvrnailics gives ver;- aearig the total power In thc rotation noise, Fron the thrcc dizfzrent methods of calculation, the powers arc Provided by IHSNot f
35、or ResaleNo reproduction or networking permitted without license from IHS-,-,-10 U.A.C.A. Technical Bote Bo. 747 Experiment, f- Pqn = 28.7 watts. Pqn = 12.3 watts, 3.68 decibels %elow 28.7 1-1 at t s . qn= 2 8 S- P,= 11.3 watts, 4.04 decibels below 28.7 qn=2 watts. 3 I S C: U S S I OB In the cov-.rs
36、e of tie experimental work connected with thzs Xiapcr, t5c question 03 interference agpeared. With the-microphone placed 5 feet above the grouzd, data were obtained that gave spad-run curvcs which wore less steep than theory indicated, particularly for the third and the fourth harmonics. The polar c
37、urves obtained with the mi- crophone ia this position did, howcver, check reasonably well. wit2 the thcory. Yith the microphone on the grouiid, the position used for tli2 d-atn presented herein, the slopes of thc spoed- run curviis vcre steeper than theory indicated cxccpt that for the fourth harmon
38、ic, which was less steep than the thoory indicr:tcd. This resuit is shown in figure 4. The slopes shown in figure 4 obtained from equations (2) and. (9) arc very ncarly the sane. Thc polar curves give a fair check for tho first and thc second- liarnonics, but the third and the fourth h?,rmonics show
39、 a discrcpaccg of about 4.6 an whereas, progressively larger values should have been used for the highcr harmonics. If larger values of B had been used in equ-atioiz (2), as Gutin suggests in his studied approxi- mations, the difference in sound. pressures obtained from equctions (2) and (9) won1d h
40、ave been sma11. As higher harmonics and z greater number of blades arc considcrcd, the thickness cffoct bccomcs more impor- tant relntive to tho thrust and the torque effect, pzrtic- ularly at high Vo/c. This conclusion is drawn from a study of the effect of (1 amid n in equations (2) and (9) compar
41、cd with tlzc effect of q nnd n in equztion ,(19) of refcrencc I. A Better approach to sxperimental data can bc obtzined by incl-cding tl;,ickncss effect than from eqation (2) or (9) aloilc. if the square root of the sum of the squares of tliz sound prcssures obtained from equation (9) and from equat
42、ion (19) of rcfcrencc 1 were calculated, better com- parison with cxperincnt sliould result. A difference in tine pL3Se occurs betircen t3c thickness cffect and tlzc tlfrust aid tqrquc effect, thc Fourier scrios for t!ie thick- ness cffect Seing a siiic scries md that for the thrust and toryuc effec
43、t being a cosiac scriqs; .CTJCC, the square root of the sun of tho squares is sugestcd. For coixvcnicncc, cquation (19) of refcrciice 1 for thickness effect is repez-ted as cquation (12) of this paper. 30” EO* - e-. 4- 2(2qr.+2) (q11-1-3) 24(2qn+.?) (2qn+4) (qnt.5) Provided by IHSNot for ResaleNo re
44、production or networking permitted without license from IHS-,-,-12 B.A.C.A. Technical Tote Bo. 7437 an f(a,%) = - - 3.b (for typical syrnnetrical airfoil. scct;io:i). d ;?, is or,e-li?clf o?axizun thickness at nlsout 0.80R,* 3, chord at about 0.80Ro* mid all of the other syn3ols are thc srme as thos
45、e used in the prcse:it paper. As e4713tioa (12) gives tic the free- space root-nenr-squaTc vclu,cs, 11 val-ucs obtaizied fron equztion (1%) nust be divided Sy fl in orcier,to 5c used vitli the values obtaincci fron equation (2) or (gj. The qucstion of solid.it;r (r is of ii2porta:rcc in de- tcmining
46、 the Fourier cocfficients : for t3c approxinations nzdc in deriving equations (2), (s), CE, but it is acliavZ2 that hnrr?oriics up to til2 order of 1/20, ome-half tic r ociprccr=l. of tlic solidit;-, C:X 135 cnlctrlztcd by equpvt;ions (a), (si, a116 (12) without serious crror froin this ccxse. Thc s
47、olidity o C:lil 3c expressed by 11b/2nR. A gooJ appeared as a result of some invcstigations of fan noise. This work in- volved low tip speeds so thzt practically 211 of the noise generated was due to vortices tx-ailinc; fron the blades# If sufficientlZ7 fii:;h vnlucs of tip s-peecL hd becn used in t
48、he tests, rotational poisc voul1: hcvc hr?cl to be considered and wol;ld hcvc Bominatcd thct acoustic spzctrum from thc fan. The importanccoT ths rotation noise qt high ti;! spccds is due to the fGct thct rotation noise gcncrally incrcsscs with ,?. grcF,tcr poser of, T0/c than coes .Tortex noise. It is found from fiGurc 4 that rotation noisc power radiated in tlic liarmonies varies nnproximntoly 8,s t:tc G .t 5/3 qn power of .v/c, but tlie power r2,ai:tca as vortex nofsc varies as approxinrtc
